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<title>Union</title>
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<h1 class="reftitle">Union</h1>
<h2>Purpose</h2>
<p>Represents a general union of convex sets in MPT</p>
<h2>Syntax</h2>
<pre class="synopsis">U = Union(Set)</pre>
<h2>Description</h2>
<p></p>
        The <tt>Union</tt> object represent collection of various convex sets. The 
        only restriction for the sets is to be convex, i.e. they have to be derived from
        the <tt>ConvexSet</tt> class.
        
        You can associate functions to any of the set via <tt>addFunction</tt> method of the 
        <tt>ConvexSet</tt> class. Function handles and all properties of the sets can be
        accessed via <tt>Union.Set</tt> property based on the index.
         
        For a list of available methods type "methods('Union')".
    <h2>Input Arguments</h2>
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<td><tt>Set</tt></td>
<td>
<p></p>Any object derived from the <tt>ConvexSet</tt> class. <p>
	    		Class: <tt>ConvexSet</tt></p>
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<h2>Output Arguments</h2>
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<td><tt>U</tt></td>
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<p></p>Object of the <tt>Union</tt> class. <p>
	    		Class: <tt>Union</tt></p>
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<h2>Example(s)</h2>
<h3>Example 
				1</h3> Construct union of two <tt>YSet</tt> objects.  Define the objects in YALMIP <pre class="programlisting"> x = sdpvar(2,1); </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> F1 = [0&lt;= x &lt;=1]; </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> F2 = [ norm(x-[1;1]) &lt;= 1]; </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> Y(1) = YSet(x,F1); </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> Y(2) = YSet(x,F2); </pre>
<pre class="programlisting"></pre> Create the union <pre class="programlisting"> U=Union(Y) </pre>
<pre class="programlisting">Union of 2 convex sets.
Functions : none
</pre> Plot the union <pre class="programlisting"> U.plot </pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/unions/@Union/union_img_1.png" alt="../../../../../../fig/mpt/modules/geometry/unions/@Union/union_img_1.png" width="60%"></p>
<h3>Example 
				2</h3> Construt the union of two polyhedra in 1D. Define the polyhedra <pre class="programlisting"> P(1) = Polyhedron('lb',-5,'ub',1); </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> P(2) = Polyhedron('lb',0); </pre>
<pre class="programlisting"></pre> Create the union <pre class="programlisting"> U = Union(P) </pre>
<pre class="programlisting">Union of 2 convex sets.
Functions : none
</pre> Plot the polyhedra <pre class="programlisting"> U.plot('linewidth',3) </pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/unions/@Union/union_img_2.png" alt="../../../../../../fig/mpt/modules/geometry/unions/@Union/union_img_2.png" width="60%"></p>
<h2>See Also</h2>
<a href="../../sets/@YSet/yset.html">yset</a>, <a href="../../sets/@Polyhedron/polyhedron.html">polyhedron</a>, <a href="../@PolyUnion/polyunion.html">polyunion</a><p></p>
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<br><p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
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